TSTP Solution File: SEU315+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU315+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 14:36:11 EDT 2022
% Result : Theorem 0.18s 0.53s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of clauses : 36 ( 11 unt; 10 nHn; 36 RR)
% Number of literals : 91 ( 0 equ; 54 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
top_str(skc5),
file('SEU315+1.p',unknown),
[] ).
cnf(2,axiom,
topological_space(skc5),
file('SEU315+1.p',unknown),
[] ).
cnf(14,axiom,
~ empty(powerset(u)),
file('SEU315+1.p',unknown),
[] ).
cnf(16,axiom,
element(skc6,powerset(the_carrier(skc5))),
file('SEU315+1.p',unknown),
[] ).
cnf(29,axiom,
element(skf7(u),powerset(the_carrier(skc5))),
file('SEU315+1.p',unknown),
[] ).
cnf(32,axiom,
~ in(skf14(u,v),u),
file('SEU315+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU315+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ in(u,skf12(v,w))
| closed_subset(u,w) ),
file('SEU315+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ in(u,skf12(v,w))
| subset(v,u) ),
file('SEU315+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU315+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ in(u,v)
| element(u,v)
| empty(v) ),
file('SEU315+1.p',unknown),
[] ).
cnf(57,axiom,
( element(u,powerset(v))
| in(skf14(v,u),u) ),
file('SEU315+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ in(u,skf12(v,w))
| in(u,powerset(the_carrier(w))) ),
file('SEU315+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ element(u,powerset(powerset(the_carrier(skc5))))
| in(skf7(u),u)
| closed_subset(skf7(u),skc5) ),
file('SEU315+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ element(u,powerset(powerset(the_carrier(skc5))))
| subset(skc6,skf7(u))
| in(skf7(u),u) ),
file('SEU315+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ in(skf7(u),u)
| ~ element(skf7(u),powerset(the_carrier(skc5)))
| ~ closed_subset(skf7(u),skc5)
| ~ subset(skc6,skf7(u))
| ~ element(u,powerset(powerset(the_carrier(skc5)))) ),
file('SEU315+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ top_str(u)
| ~ topological_space(u)
| ~ element(v,powerset(the_carrier(u)))
| ~ closed_subset(v,u)
| ~ subset(w,v)
| ~ element(w,powerset(the_carrier(u)))
| ~ in(v,powerset(the_carrier(u)))
| in(v,skf12(w,u)) ),
file('SEU315+1.p',unknown),
[] ).
cnf(81,plain,
( ~ in(u,v)
| element(u,v) ),
inference(mrr,[status(thm)],[54,34]),
[iquote('0:MRR:54.2,34.0')] ).
cnf(82,plain,
( ~ element(u,powerset(powerset(the_carrier(skc5))))
| ~ subset(skc6,skf7(u))
| ~ in(skf7(u),u)
| ~ closed_subset(skf7(u),skc5) ),
inference(mrr,[status(thm)],[79,29]),
[iquote('0:MRR:79.1,29.0')] ).
cnf(83,plain,
( ~ topological_space(u)
| ~ top_str(u)
| ~ subset(v,w)
| ~ closed_subset(w,u)
| ~ in(w,powerset(the_carrier(u)))
| ~ element(v,powerset(the_carrier(u)))
| in(w,skf12(v,u)) ),
inference(mrr,[status(thm)],[80,81]),
[iquote('0:MRR:80.2,81.1')] ).
cnf(120,plain,
( ~ top_str(skc5)
| ~ topological_space(skc5)
| ~ closed_subset(u,skc5)
| ~ subset(skc6,u)
| ~ in(u,powerset(the_carrier(skc5)))
| in(u,skf12(skc6,skc5)) ),
inference(res,[status(thm),theory(equality)],[16,83]),
[iquote('0:Res:16.0,83.4')] ).
cnf(154,plain,
( in(skf7(u),powerset(the_carrier(skc5)))
| empty(powerset(the_carrier(skc5))) ),
inference(res,[status(thm),theory(equality)],[29,53]),
[iquote('0:Res:29.0,53.0')] ).
cnf(166,plain,
in(skf7(u),powerset(the_carrier(skc5))),
inference(mrr,[status(thm)],[154,14]),
[iquote('0:MRR:154.1,14.0')] ).
cnf(167,plain,
( ~ closed_subset(u,skc5)
| ~ in(u,powerset(the_carrier(skc5)))
| ~ subset(skc6,u)
| in(u,skf12(skc6,skc5)) ),
inference(mrr,[status(thm)],[120,1,2]),
[iquote('0:MRR:120.0,120.1,1.0,2.0')] ).
cnf(803,plain,
( element(skf12(u,v),powerset(w))
| in(skf14(w,skf12(u,v)),powerset(the_carrier(v))) ),
inference(res,[status(thm),theory(equality)],[57,75]),
[iquote('0:Res:57.1,75.0')] ).
cnf(1072,plain,
element(skf12(u,v),powerset(powerset(the_carrier(v)))),
inference(res,[status(thm),theory(equality)],[803,32]),
[iquote('0:Res:803.1,32.0')] ).
cnf(1108,plain,
( ~ subset(skc6,skf7(skf12(u,skc5)))
| ~ in(skf7(skf12(u,skc5)),skf12(u,skc5))
| ~ closed_subset(skf7(skf12(u,skc5)),skc5) ),
inference(res,[status(thm),theory(equality)],[1072,82]),
[iquote('0:Res:1072.0,82.0')] ).
cnf(1109,plain,
( subset(skc6,skf7(skf12(u,skc5)))
| in(skf7(skf12(u,skc5)),skf12(u,skc5)) ),
inference(res,[status(thm),theory(equality)],[1072,78]),
[iquote('0:Res:1072.0,78.0')] ).
cnf(1110,plain,
( in(skf7(skf12(u,skc5)),skf12(u,skc5))
| closed_subset(skf7(skf12(u,skc5)),skc5) ),
inference(res,[status(thm),theory(equality)],[1072,77]),
[iquote('0:Res:1072.0,77.0')] ).
cnf(1112,plain,
closed_subset(skf7(skf12(u,skc5)),skc5),
inference(mrr,[status(thm)],[1110,51]),
[iquote('0:MRR:1110.0,51.0')] ).
cnf(1113,plain,
( ~ subset(skc6,skf7(skf12(u,skc5)))
| ~ in(skf7(skf12(u,skc5)),skf12(u,skc5)) ),
inference(mrr,[status(thm)],[1108,51]),
[iquote('0:MRR:1108.2,51.1')] ).
cnf(1574,plain,
( subset(skc6,skf7(skf12(u,skc5)))
| subset(u,skf7(skf12(u,skc5))) ),
inference(res,[status(thm),theory(equality)],[1109,52]),
[iquote('0:Res:1109.1,52.0')] ).
cnf(1575,plain,
subset(skc6,skf7(skf12(skc6,skc5))),
inference(fac,[status(thm)],[1574]),
[iquote('0:Fac:1574.0,1574.1')] ).
cnf(1645,plain,
( ~ closed_subset(skf7(skf12(skc6,skc5)),skc5)
| ~ in(skf7(skf12(skc6,skc5)),powerset(the_carrier(skc5)))
| ~ subset(skc6,skf7(skf12(skc6,skc5)))
| ~ subset(skc6,skf7(skf12(skc6,skc5))) ),
inference(res,[status(thm),theory(equality)],[167,1113]),
[iquote('0:Res:167.3,1113.1')] ).
cnf(1650,plain,
( ~ closed_subset(skf7(skf12(skc6,skc5)),skc5)
| ~ in(skf7(skf12(skc6,skc5)),powerset(the_carrier(skc5)))
| ~ subset(skc6,skf7(skf12(skc6,skc5))) ),
inference(obv,[status(thm),theory(equality)],[1645]),
[iquote('0:Obv:1645.2')] ).
cnf(1651,plain,
$false,
inference(mrr,[status(thm)],[1650,1112,166,1575]),
[iquote('0:MRR:1650.0,1650.1,1650.2,1112.0,166.0,1575.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU315+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 05:43:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.53
% 0.18/0.53 SPASS V 3.9
% 0.18/0.53 SPASS beiseite: Proof found.
% 0.18/0.53 % SZS status Theorem
% 0.18/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.53 SPASS derived 1455 clauses, backtracked 4 clauses, performed 3 splits and kept 673 clauses.
% 0.18/0.53 SPASS allocated 104857 KBytes.
% 0.18/0.53 SPASS spent 0:00:00.19 on the problem.
% 0.18/0.53 0:00:00.03 for the input.
% 0.18/0.53 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.53 0:00:00.02 for inferences.
% 0.18/0.53 0:00:00.00 for the backtracking.
% 0.18/0.53 0:00:00.06 for the reduction.
% 0.18/0.53
% 0.18/0.53
% 0.18/0.53 Here is a proof with depth 5, length 36 :
% 0.18/0.53 % SZS output start Refutation
% See solution above
% 0.18/0.53 Formulae used in the proof : s3_subset_1__e1_40__pre_topc existence_m1_subset_1 fc1_subset_1 l71_subset_1 antisymmetry_r2_hidden t7_boole s1_xboole_0__e1_40__pre_topc__1 fc1_xboole_0 d2_subset_1
% 0.18/0.53
%------------------------------------------------------------------------------